In the image, point A marks the center of the circle. Which two lengths must form a ratio of 1:2?

Diagram shows a circle centered at A. Diameters EF and GI is drawn. Radius AD is drawn between points G and F. Chord BC is drawn that intersects diameter EF.

A.
AF:AE
B.
BC:EF
C.
EF:AI
D.
AI:EF
E.
AI:AD

1 answer

The correct answer is A. AF:AE.

We can see from the diagram that AF and AE are both radii of the circle with center A. Therefore, they are equal in length.

Since radii of a circle are always equal in length, the ratio of AF to AE will always be 1:1 or simply 1.

None of the other options (BC:EF, EF:AI, AI:EF, AI:AD) involve lengths that are necessarily equal to each other, so they cannot have a ratio of 1:2.
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